To find the error interval for $x$ when $x$ is rounded to two decimal places as $15.31$, we should consider the range of values that could round to $15.31$.

Solution:

1. Identify the rounding rule: Since $x$ is rounded to two decimal places, any number in the range from $15.305$ to $15.315$ will round to $15.31$.

2. Define the interval:

   • The lower bound (inclusive) is $15.305$.
   • The upper bound (exclusive) is $15.315$.

Final Answer:

The error interval for $x$ is: $15.305 \leq x < 15.315$

Would you like more details on how to find error intervals?

Here are five related questions for further exploration:

1. What is the error interval for a number rounded to one decimal place, for example, $8.4$?
2. How would the error interval change if $x$ was rounded to three decimal places instead of two?
3. Can you explain how to determine error intervals for different rounding methods, such as rounding up or down?
4. How does an error interval differ from a confidence interval in statistics?
5. What are some practical applications of error intervals in measurement and science?

Tip: Remember that error intervals represent all possible values a rounded number could have been before rounding. This helps ensure accuracy in scientific measurements and calculations.